Incremental Kernel PCA for Online Learning of Feature Space

In this paper, a feature extraction method for online classification problems is presented by extending Kernel Principal Component Analysis (KPCA). The proposed incremental KPCA (IKPCA) constructs a nonlinear highdimensional feature space incrementally by not only updating eigen-axes but also adding new eigen-axes. The augmentation of a new eigen-axis is carried out when the accumulation ratio falls below a threshold value. We mathematically derive the incremental update equations of eigen-axes and the accumulation ratio without keeping all training samples. From the experimental results, we conclude that the proposed IKPCA works well as an incremental learning algorithm of a feature space in the sense that a minimum number of axes are augmented to maintain a designated accumulation ratio, and that the eigenvectors with major eigenvalues can converge closely to those of the batch type of KPCA. In addition, the recognition accuracy of IKPCA is similar to or slightly better than that of KPCA.